Energy Storage Part 9 potx

Multi-Area Frequency and Tie-Line Power Flow Control by Fuzzy Gain Scheduled SMES 95 system frequency but the system oscillates for longer times. Decreasing the value of K I yields comparatively higher maximum frequency deviation at the beginning but provides very good damping in the later cycles. These initiate a variable K I , which can be determined from the frequency error and its derivative. Obviously, higher values of K I is needed at the initial stage and then it should be changed gradually depending on the system frequency changes. Fig. 7. Frequency deviation step response for different values of K I Dynamic performance of the AGC system would obviously depend on the value of frequency bias factors, β 1 = β 2 =B and integral controller gain value, K I1 =K I2 =K I . In order to optimize B and K I the concept of maximum stability margin is used, evaluated by the eigen- values of the closed loop control system. For a fixed gain supplementary controller, the optimal values of K I and B are chosen, here, on the basis of a performance index (PI) given in (10) for a specific load change. The Performance Index (PI) curves are shown in Fig. 8 without considering governor dead-band (DB) and generation rate constraints (GRC). () T 222 tie 1 1 2 2 0 PI ΔPwΔfwΔfdt=++ ∫ (10) Where, w 1 and w 2 are the weight factors. The weight factors w 1 and w 2 both are chosen as 0.25 for the system under consideration [Sheikh et al., 2008]. From Fig. 8, in the absence of DB & GRC it is observed that the value of integral controller gain, K I = 0.34 and frequency bias factors, B=0.4 which occurs at PI = 0.009888. 0 2 4 6 8 10 12 -8 -6 -4 -2 0 2 4 6 x 10 -4 Time [sec] Frequency deviation [Hz] K I =0 K I =1 Energy Storage 96 0.1 0.2 0.3 0.4 0.5 0.6 0.0095 0.01 0.0105 0.011 0.0115 0.012 0.0125 0.013 Integral Gain (K I ) Performance Index (PI) B=0.1 B=0.15 B=0.2 B=0.25 B=0.3 B=0.35 B=0.4 B=0.45 B=0.5 Without GRC and Gov. Deadband K I =0.34 and B=0.4 at PI=0.0099 Fig. 8. The optimal integral controller gain, K I and frequency bias factor, B 6. Control system design 6.1 Fuzzy gain schedule PI controller for AGC [Sheikh et al., 2008] Figure 9 shows the membership functions for PI control system with a fuzzy gain scheduler. The approach taken here is to exploit fuzzy rules and reasoning to generate controller parameters. The triangular membership functions for the proposed fuzzy gain scheduled integral (FGSPI) controller of the three variables (e t , t ce  , K I ) are shown in Fig. 9, where frequency error (e t ) and change of frequency error ( t ce  ) are used as the inputs of the fuzzy logic controller. K Ii is the output of fuzzy logic controller. Considering these two inputs, the output of gain K Ii is determined. The use of two input and single output variables makes the design of the controller very straightforward. A membership value for the various linguistic variables is calculated by the rule given by ( ) ( ) ( ) μ e,ce =minμ e,μ ce tt t t ⎡ ⎤ ⎣ ⎦  (11) The equation of the triangular membership function used to determine the grade of membership values in this work is as follows: () ( ) b-2 x-a Ax= b (12) Where A(x) is the value of grade of membership, ‘b’ is the width and ‘a’ is the coordinate of the point at which the grade of membership is 1 and ‘x ‘ is the value of the input variables. The control rules for the proposed strategy are very straightforward and have been developed from the viewpoint of practical system operation and by trial and error methods. Multi-Area Frequency and Tie-Line Power Flow Control by Fuzzy Gain Scheduled SMES 97 The membership functions, knowledge base and method of defuzzification determine the performance of the FGSPI controller in a multi-area power system as shown in (13). Mamdani’s max-min method is used. The center of gravity method is used for difuzzification to obtain K I . The entire rule base for the FGSPI controller is shown in Table I. n μ u jj j=1 K= n I μ j j=1 ∑ ∑ (13) Fig. 9. Membership functions for the fuzzy variables e ce NB NS Z PS PB NB PB PB PB PS Z NS PB PB PS Z NS Z PB PS Z NS NB PS PS Z NS NB NB PB Z NS NB NB NB Table 1. Fuzzy Rule base for FGSPI Controller μ [e t (x)] NB NS Z PS PB μ [de t (x)/dt] NB NS Z PS PB μ [K Ii (x)] NB NS Z PS PB -0.1 -0.05 0 0.05 0.1 e t (x) 1 0.75 0.32 0.01 0.001 K I (x) -0.03 -0.015 0 0.015 0.03 de t (x)/dt 1 1 1 Energy Storage 98 6.2 Control strategy for SMES Figure 10 outlines the proposed simple control scheme for SMES, which is incorporated in each control area to reduce the instantaneous mismatch between the demand and generation, where I sm , V sm and P sm are SMES current, SMES voltage and SMES power respectively. For operating point change due to load changes, gain (K Ii ) scheduled supplementary controller is proposed. Firstly K Ii is determined using the fuzzy controller to obtain frequency deviation, Δf, and tie-line power deviation, ΔPtie. Finally ACE i which is the combination of ΔPtie and Δf [as shown in (9)] is used as the input to the SMES controller. It is desirable to restore the inductor current to its rated value as quickly as possible after a system disturbance, so that the SMES unit can respond properly to any subsequent disturbance. So inductor current deviation is sensed and used as negative feedback signal in the SMES control loop to achieve quick restoration of current and SMES energy levels. Fig. 10. Superconducting magnetic energy storage unit control system 7. Simulation results To demonstrate the usefulness of the proposed controller, computer simulations were performed using the MATLAB environment under different operating conditions. The system performances with gain scheduled SMES and fixed gain SMES are shown in Fig. 11 through Fig. 14. Two case studies are conducted as follows: Case I: a step load increase (ΔP L2 =0.01 pu) is considered in area2 only. It is seen from Fig. 11 that, the tie line power deviation are more reduced with the proposed gain scheduled controller than the fixed gain one including SMES, and the deviations are positive in Case I. Thus sensing the input signal ACE i in both the control areas SMES provide sufficient compensation as shown in Fig. 12, where in area1 SMES is charging/discharging energy and area2 SMES is discharging/charging energy to keep the frequency deviations in both areas minimum. From Fig. 12 it is seen that, fuzzy gain scheduled integral controller of the loaded area determines the integral gain, K I , to a scheduled value to resotore the frequency to its nominal value, and fuzzy gain scheduled integral controller of the unloaded area reamains unscheduled and selects the critical value dc 0 sT1 K + dc id sT1 K + sLR 1 L + Δ I sm I sm Δ V sm Δ V sm P sm ACE i Π +- + + I sm0 V sm0 + V sm + + + Multi-Area Frequency and Tie-Line Power Flow Control by Fuzzy Gain Scheduled SMES 99 0 5 10 15 -1 0 1 2 3 4 x 10 -3 Time [sec] Tie-power deviation [pu MW] Gain Scheduled+SMES Fixed gain+SM ES Fig. 11. Performances of tie power deviation for a step load increase ∆P L2 =0.01 pu in area2 only -0.01 -0.008 -0.006 -0.004 -0.002 0 A rea- 1 Frequency deviation [Hz] Gain Scheduled+SM ES Fixed gain+SM ES -0.015 -0.01 -0.005 0 A rea- 2 Gain Scheduled+SM ES Fixed gain+SMES 0 0.5 1 Ki Variation 0.2 0.4 0.6 0.8 1 4.85 4.9 4.95 Ism deviation [kA] 3.5 4 4.5 5 0 5 10 15 -4 -2 0 2 4 6 x 10 -4 Psm [MW] Time [sec] 0 5 10 15 -6 -4 -2 0 2 x 10 -3 Time [sec] Fig. 12. System performances for a step load increase ∆P L2 =0.01 pu in area2 only Energy Storage 100 0 5 10 15 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 x 10 -3 Time [sec] Tie-power deviation [pu MW] Gain Scheduled+SM ES Fixed gain+SM ES Fig. 13. performances of tie power deviation for a step load increase ∆P L1 =0.015 pu in area1 & ∆P L2 = 0.01 pu in area2 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 Area-1 Frequency deviation [Hz] Gain Scheduled+SMES Fixed gain+SM ES -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 Area-2 Gain Scheduled+SMES Fixed gain+SMES 0.2 0.4 0.6 0.8 1 Ki Variation 0.2 0.4 0.6 0.8 1 2.5 3 3.5 4 4.5 5 Ism deviation [kA] 3.5 4 4.5 5 0 5 10 15 -10 -5 0 5 x 10 -3 Psm [MW] Time [sec] 0 5 10 15 -6 -4 -2 0 2 x 10 -3 Time [sec] Fig. 14. System performances for a step load increase ∆P L1 =0.015 pu in area1 & ∆P L2 = 0.01 pu in area2 Multi-Area Frequency and Tie-Line Power Flow Control by Fuzzy Gain Scheduled SMES 101 as its integral gain. In addition, it is seen that, the damping of the system frequency is not satisfactory in the case with the fixed gain controller including SMES, but the proposed gain scheduled supplementary controller including SMES significantly improves the system performances. Case II: different step load increase is applied to each area. In this case, as each area is loaded by the different load increase, each area adjusts their own load. Fig. 13 shows the tie power deviation but the magnitude is small. So the SMES controller in both areas dominated on Δf i . As ΔP L1 =0.015 pu & ΔP L2 =0.01 pu, it is seen from Fig. 14 that SMES in area1 provided more compensation than that in area2. The inductor current deviation ( ΔI sm ) is also reduced significantly and return back to the rated value quickly with the proposed control system. Finally, it is seen from Fig. 14 that fuzzy gain scheduled integral controller of both the loaded areas determine the integral gain K Ii to a scheduled value to resotore the frequency to its nominal value. Due to this, the damping of the system frequency is also improved with the proposed FGSPI controller including SMES. 8. Chapter conclusions The chapter discussed about the simulation studies that have been carried out on a two-area power system to investigate the impact of the proposed intelligently controlled SMES on the improvement of power system dynamic performances. The results clearly show that the scheme is very powerful in reducing the frequency and tie-power deviations under a variety of load perturbations. On-line adaptation of supplementary controller gain associated with SMES makes the proposed intelligent controllers more effective and are expected to perform optimally under different operating conditions. 9. References Benjamin, NN. & Chan, WC. (1978). Multilevel Load-frequency Control of Inter-Connected Power Systems, IEE Proceedings, Generation, Transmission and Distribution,Vol. No.125, pp.521–526. Nanda, J. & Kavi, BL. (1988). Automatic Generation Control of Interconnected Power System, IEE Proceedings, Generation, Transmission and Distribution, Vol. 125, No. 5, pp.385–390. Das, D.; Nanda, J.; Kothari, ML. & Kothari, DP. (1990). Automatic Generation Control of Hydrothermal System with New Area Control Error Considering Generation Rate Constraint, Electrical Machines and Power System, Vol. 18, pp.461–471. Mufti, M. U.; Ahmad Lone, S.; Sheikh, J. I. & Imran, M. (2007). Improved Load Frequency Control with Superconducting Magnetic Energy Storage in Interconnected Power System, IEEJ Transactions on Power and Energy, Vol. 2, pp. 387-397. Nanda, J.; Mangla, A & Suri, S. (2006). Some New Findings on Automatic Generation Control of an Interconnected Hydrothermal System with Conventional Controllers, IEEE Transactions on Energy Conversion, Vol. 21, No. 1, pp. 187-194, (March, 2006). Oysal, Y.; Yilmaz, A.S. & Koklukaya, E. (2004). Dynamic Fuzzy Networks Based Load Frequency Controller Design in Electrical Power Systems, G.U. Journal of Science, Vol. 17, No. 3, pp. 101-114 Benjamin, NN. & Chan WC. (1982). Variable Structure Control of Electric Power Generation. IEEE Transactions on Power Apparatus and System, Vol. 101, No. 2, pp.376–380. Energy Storage 102 Sivaramaksishana, AY.; Hariharan, MV. & Srisailam, MC. (1984). Design of Variable Structure Load-Frequency Controller Using Pole Assignment Techniques, International Journal of Control, Vol. 40, No. 3, pp.437–498. Tripathy, SC, & Juengst, KP. (1997). Sampled Data Automatic Generation Control with Superconducting Magnetic Energy Storage, IEEE Transactions on Energy Conversion Vol. 12, No. 2, pp.187–192. Shayeghi, H. & Shayanfar, H.A. (2004). Autometic Generation Control of Interconnected Power System Using ANN Technique Based on μ-Synthesis, Journal of Electrical Engineering , Vol. 55, No. 11-12, pp. 306-313. Sheikh, M.R.I.; Muyeen, S.M.; Takahashi, R.; Murata, T. & Tamura, J. (2008). Improvement of Load Frequency Control with Fuzzy Gain Scheduled Superconducting Magnetic Energy Storage Unit, International Conference of Electrical Machine (ICEM, 08), (06-09 September, 2008), Vilamura, Portugal. Demiroren, A. (2002). Application of a Self-Tuning to Automatic Generation Control in Power System Including SMES Units, European Transactions on Electrical Power, Vol. 12, No. 2, pp. 101-109, (March/April 2002). IEEE Task Force on Benchmark Models for Digital Simulation of FACTS and Custom–Power Controllers, T&D Committee, (2006). Detailed Modeling of Superconducting Magnetic Energy Storage (SMES) System, IEEE Transactions on Power Delivery, Vol. 21, No. 2, pp. 699-710, (April 2006). Ali, M. H.; Murata, T. & Tamura, J. (2008). Transient Stability Enhancement by Fuzzy Logic- Controlled SMES Considering Coordination with Optimal Reclosing of Circuit Breakers, IEEE Transactions on Power Systems, Vol. 23, No. 2, pp. 631-640, (May 2008). http://www.doc.ic.ac.uk/~matti/ise 2grp/energystorage_report/node8.html http://en.wikipedia.org/wiki/Superconducting_magnetic_energy_storage Demiroren, A. & Yesil, E. (2004). Automatic Generation Control with Fuzzy Logic Controllers in the Power System Including SMES Units, International Journal of Electrical Power & Energy Systems, Vol. 26, pp. 291-305. Abraham, R.J.; Das, D. & Patra, A. (2008). AGC Study of a Hydrothermal System with SMES and TCPS, European Transactions on Electrical Power, DOI: 10.1002/etep.235 Wu, C. J. & Lee, Y. S. (1991). Application of Superconducting Magnetic Energy Storage to Improve the Damping of Synchronous Generator, IEEE Transactions on Energy Conversion, Vol. 6, No. 4, pp. 573-578, (December 1991). Banerjee, S.; Chatterjee, J. K. & Tripathy, S. C. (1990). Application of Magnetic Energy Storage Unit as Load Frequency Stabilizer, IEEE Transactions on Energy Conversion, Vol. 5, No. 1, pp. 46-51, (March 1990). M.R.I. Sheikh was born in Sirajgonj, Bangladesh on October 31, 1967. He received his B.Sc. Eng. and M.Sc. Eng. Degree from Rajshahi University of Engineering & Technology (RUET), Bangladesh, in 1992 and 2003 respectively, all in Electrical and Electronic Engineering. He is currently an Associate Professor in the Electrical and Electronic Engineering Department, RUET. Presently he is working towards his Ph.D Degree at the Kitami Institute of Technology, Hokkaido, Kitami, Japan. His research interests are, Power System Stability Enhancement Including Wind Generator by Using SMES, FACTs devices and Load Frequency Control of multi-area power system. Mr. Sheikh is the member of the IEB and the BCS of Bangladesh. 6 Influence of Streamer-to-Glow Transition on NO Removal by Inductive Energy Storage Pulse Generator Koichi Takaki Iwate University Japan 1. Introduction Huge amounts of air pollutants like carbon monoxide, unburned hydrocarbons, nitrogen oxides (NOx), and particulate matter have been released into the atmosphere by various sources such as coal, oil, and natural gas-burning electric power generating plants, motor vehicles, diesel engine exhaust, paper mills, metal and chemical production plants, etc., over the last several decades. These pollutants are the main cause of acid rain, urban smog, and respiratory organ disease (Chang, 2001). For pollutants emitted from motor vehicle, the exhaust of gasoline engines is cleaned effectively with the three-way catalyst. However, for diesel and lean burn engines, the three-way-catalyst does not work because the high oxygen content in the exhaust gases prevents the reduction of nitrogen oxide (NO) (Clements et al., 1989). Dry NOx removal technology is one of the conventional processes which may provide a potential solution for such problems (Eliasson and Kogelschatz, 1991). A non-thermal plasma process using a pulse streamer corona discharge is particularly attractive for this purpose (Namihira et al., 2000). During the past decade, numerous studies on this process have been conducted using a diesel engine exhaust gas and/or a simulated gas (Hackam & Akiyama, 2000). Although encouraging results have been obtained from the experiments, it is urgent to design a whole removal system compact enough for vehicle application. Two methods for storing energy are employed in high-power pulse generators: capacitive and inductive storages. When the energy is stored in capacitors, the energy is transferred to a load through closing devices, e.g., high-current nanosecond switches. If the energy is stored in an inductive circuit with current, opening switch is used to transfer energy to a load (Rukin, 1999). For short-pulsed high voltage generation with high impedance load, inductive energy storage (IES) system is more adequate than capacitive energy storage system, if appropriate opening switches are available (Jiang et al., 2007). High-voltage nanosecond pulse generators, in which high-voltage semiconductor diodes are employed for interrupting currents stored as inductive energy, have been developed (Rukin, 1999). The generators using the high-voltage diodes as semiconductor opening switch (SOS) have an all-solid-state switching system and therefore, combine high pulse repetition rate, stability of the output parameters and long lifetime (Grekhov & Mesyats, 2002). SOS pulse generators operating at various institutions demonstrated their high reliability during Energy Storage 104 applied research work connected with the pumping of gas lasers (Baksht et al., 2002), ionization of air with a corona discharge (Yalandin, et al., 2002, Cathey, et al., 2007), generation of radical species with a atmospheric pressure glow discharge (Takaki, et al., 2005), and generation of high-power microwave (Bushlyakov et al., 2006). The streamer discharges driven by a pulsed power generator can dissociate oxygen molecules to atomic oxygen radicals with high-energy efficiency because of low-conductive current loss (Fukawa et al., 2008). The IES pulsed power generator using SOS diodes is particularly attractive for this purpose because the whole system can be compact, lightweight and driven at high repetition rate. However, a discharge produced by the IES pulsed power generator transients from streamer to glow when the energy stored in the capacitor still remains after the energy transfer from a capacitor to an inductor at opening the SOS diodes (Grekhov & Mesyats, 2002). As the results, the energy efficiency for gas treatment using non-thermal plasma is affected by the streamer-to-glow transition (Takaki et al., 2007). In here, NO removal using a co-axial type non-thermal plasma reactor driven by an IES pulsed power generator is described. The influence of streamer-to-glow transition on NO removal in the non-thermal plasma reactor is also described. 2. Experimental setup Figure 1(a) shows the schematics of the experimental circuit. The IES pulsed power generator consists of a primary energy storage capacitor C, a closing switch SW, a secondary energy storage inductor L, and an opening switch. The circuit current flows to the LC circuit governed by the following equation after closing the switch SW (Robiscoe et al., 1998): 0 2 0 0 sin R t L V ie t L ω ω − = , (1) 2 0 1 2 R LC L ω ⎛⎞ =− ⎜⎟ ⎝⎠ , (2) where t is the time from the activation of the closing switch, V 0 is the charged voltage, L is the inductance of the energy storage inductor, C is the capacitance of the primary energy storage capacitor, and R is the circuit resistance (R < 4 L / C). When SOS diodes are used as an opening switch as shown in Figure 1(a), the circuit current flows through the SOS diodes as a forward-pumping current during a half period F TLC π ≈ of LC oscillation (Yalandin et al., 2000). After the current direction reverses with LC oscillation, the reverse current is injected into the SOS during the period T R . After the injection phase T R , the circuit current is interrupted by a short duration T O . With the current interrupted by the SOS, a high-voltage pulse is produced as follows: 0 1 out di di VV idtL RiL Cdt dt =− − −≈− ∫ , (3) as shown in Fig. 1(b). This pulse voltage can be applied to a load as a short nanosecond pulse (Takaki et al., 2005, Rukin, 1999, Yankelevich & Pokryvailo, 2002). [...]... applied to the reactor This result indicates the energy stored in the capacitor is almost released through LC oscillation Figure 4 also shows time-dependency of energy stored in the secondary energy storage inductor EL, energy stored in the primary energy storage capacitor EC, energy loss in the SOS diodes ESOS and energy consumed in the reactor Eload The energy stored in the capacitor is transferred... oscillation After that, the energy stored in the inductor is transferred back to the capacitor in next quarter cycle The energy of 16 mJ is consumed in the SOS in the period of LC half cycle because of the resistive component of the SOS diodes The total energy transfer from the primary energy storage capacitor to the reactor is around 20% under the circuit condition The energy transfer efficiency changes... capacitance of the primary energy storage capacitor C and the inductance of the secondary energy storage inductor L were changed in range from 0.12 to 4.2 nF and from 4.8 to 18.5 μF, respectively, as shown in Table 1 The charging voltages of the capacitor C were -20 kV for conditions 1-3 and -12 kV for condition 4 The pulse repetition rate was changed to control the input energy in the reactor The current...Influence of Streamer-to-Glow Transition on NO Removal by Inductive Energy Storage Pulse Generator 105 I0 SW L 0 TF TR TO V0 SOS diode C t I0 V out V out 0 (a) t (b) Fig 1 Schematic of an inductive energy storage pulse power generator with semiconductor opening switch: (a) equivalent circuit; (b) circuit current and output voltage Fast... reactor voltage Vout and the voltage of the primary energy storage capacitor VC with connection of the pulsed power generator to the reactor The circuit condition is chosen as C=0.68 nF and L=1.4 μH The charging voltage V0 of the capacitor is set to be -20 kV The discharge current Iload can be divided by two parts; displacement current at the early part of the current and a discharge current as the... voltage is 25 ns in FWHM (full-width at half-maximum) The total inductance of the circuit is the summation of the secondary energy storage inductor and a circuit loop inductance The total circuit inductance can be roughly estimated using the equation TF ≈ π LC and is calculated to be 9. 6 μH using a 210 ns half period of LC oscillation This inductance and rapid current interruption produces a high voltage... schematic of the experimental set-up using the pulse streamer discharge reactor The simulated gas was diluted NO with nitrogen and oxygen mixed with ratio of 9: 1 The co-axial plasma reactor consists of a 1mmφ tungsten wire and a copper cylinder 106 Energy Storage Inlet Coaxial Reactor Flow controler ID Mixture Vessel NO + N2 outlet V out O2 Gas Analyzar V C I0 Fig 2 Experimental setup for NO removal from... 150 ns using values of C and L of the conditions 1, 2, and 3, respectively The measured period TF shows a larger value than those Influence of Streamer-to-Glow Transition on NO Removal by Inductive Energy Storage Pulse Generator 20 Voltage [kV] 80 TR TF 10 Vout 0 0 -10 VC -20 -30 40 -40 C =0.48 nF L =4.8 μH I0 0 Current [A] 30 107 0.1 0.2 Time [μs] 0.3 -80 Fig 3 Typical waveforms of circuit current... digitizing oscilloscope (500 MHz band width, 5 GS/s sampling rate) was transmitted to a computer through a LAN cable for calculating the energy consumed in reactor Condition #1 #2 #3 #4 C [nF] 0.12 0.23 0.48 4.2 L [μH] 18.5 10.5 4.8 12.6 TF [ns] 203 205 224 876 TR [ns] 67 68 69 102 Table 1 Forward and reversed pumping time of SOS diodes for various circuit parameters Figure 2 shows a schematic of the experimental... circuit condition The energy transfer efficiency changes by changing circuit parameter as reported in the reference (Takaki et al., 2007) The energy transfer efficiency increases to 40% by decreasing circuit current from 200 to 50 A in peak value because the energy loss in the SOS decreases with decreasing current through the SOS diodes . 573-578, (December 199 1). Banerjee, S.; Chatterjee, J. K. & Tripathy, S. C. ( 199 0). Application of Magnetic Energy Storage Unit as Load Frequency Stabilizer, IEEE Transactions on Energy Conversion,. Juengst, KP. ( 199 7). Sampled Data Automatic Generation Control with Superconducting Magnetic Energy Storage, IEEE Transactions on Energy Conversion Vol. 12, No. 2, pp.187– 192 . Shayeghi, H Wu, C. J. & Lee, Y. S. ( 199 1). Application of Superconducting Magnetic Energy Storage to Improve the Damping of Synchronous Generator, IEEE Transactions on Energy Conversion, Vol. 6, No.